Feature Detection and Description: Techniques and Algorithms, Exams of Computer Science

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Feature Detection

Features

• Places where intensities vary is some prescribed way in a small neighborhood
• How to quantify this variability
  • Derivatives – direcitonal derivatives, magnitudes - Scale and smoothing
  • Statistics
    • Variance of some property (Gaussian weights on neighborhood)

Other Types of Features

• Lines (contrast, width, orientation)
• Corners (contrast, angle, orientation)
• Ridges/valleys
• Line ends f

Edges

• Places of “sharp” change in brightness
• How to quantify this…
• In 1D - model
  • Gauss conv w/step
    • f(x) = g(x)*s(x)
    • Derivative of step is delta

Generalizing To Multiple

Dimensions

• Marr-Hildreth
  • Gradient threshold
  • Zero crossings in the Laplacian of f(x)
  • f xx (x) + f yy (x) = 0 ; f x (x) 2 + f y (x) 2 > T 2
• Canny Edges (1980s)
  • Do nonmaximal suppression along the direction of the gradient

Canny Edges

• Preprocessing - denoising
• Derivatives - computed with kernels
• Zero crossings - 8-connected thin lines
• Hysterises thresholding (on gradient)
  • All pixels that satisfy zero-crossing and gradient

    Thi are edges - All accept all pixels that in the Thi connected components using Tlo - Lower gradient edges can be brought in if they are connected to high-gradient edges Thi –> edges Tlo –> not edges Tlo –> edges

Connected Component

• A subset S of pixels in an image such that
  • For any pair of pixels [(a),(b)] E S, there exists a k-connected path between (a) and (b).
• Usefulness: find connected components S in an image that satisfy some conditions - Pixel conditions P(a) - Threshold or some other grey-level test - Region conditions R(S) - Aggregate quantities such as size, length, etc.
• Algorithm: flood fill

Flood Fill

• Highlight regions in an image
• “Test(i, j)” - is value at pixel (i,j) between a and b
• Inputs: seed, values a&b
• Data structures: input array, output array, list of grid points to be processed

Corners

• Places where gradient directions vary (at some scale) - + high gradient (edge) possibly
• How to capture this…

Level Sets of an Image

• Level set – set of points f(x, y)=k
  • “isophote”, “isocontour”, “isosurface”(3D) Family of embedded contours Greyscale image

Corners – differential approach

• High derivative of normal in direction perpendicular to gradient
• This is level-set/isophote curvature–κ

Corners – differential approach

• Non-maximal supression
• Or local max of
  • Compare to neighbors
    • Canny edge Has a “sign” convex/concave

Finding Local Point Maxima

• Zero crossings of x and y derivatives
• Pixel greater than its neighbors (4 or 8 connected)
• Threshold and find center of mass of connected component

VISPack Code

im = im.gaussDiffuse(3.0); im_dx = im.dx(); im_dy = im.dy(); grad_mag = (im_dx.power(2) + im_dy.power(2)).sqrt(); curve = (im.dx(2)im_dy.power(2) + im.dy(2)im_dx.power(2) - 2.0im_dx.dy()im_dxim_dy).abs() /(grad_mag.power(2) + (float)1.0e-2); curve = curve.setBorder(0.0f, 2); curve = grad_magcurve.abs();